Question

The perimeter of a rectangular field is 130m if it's length is 5m more than its breath find the length and breadth of the field

Answer 1

Perimeter = 130 m.
Let the breadth be x m.
Then the length will be x+5 m.

We know that,

Perimeter of a rectangle = 2(length+breadth).

So, on substituting the values:

130 = 2[(x+5)+x].

Transposing 2 to LHS:

130/2 = (x+5) +x.
65 = 2x+5.

Transposing 5 to LHS:

65-5 = 2x.
60 = 2x.

Transposing 2 to LHS:

60/2 = x.
x = 30 m.
x+5 = 35 m.

Therefore, the length is 35 m and the breadth is 30 m.

Answer 2

⠀⠀⠀⠀

Given:

• The Perimeter of the rectangular field is 130m. & it's Length is 5m more than it's breadth.

Need to Calculate:

• The dimensions of the field?

❍ Let's say, that the Breadth of the field be x m. Then, it's Length be (x + 5) m respectively.

⠀

To find the dimensions of the given rectangular field, we can use the Perimeter formula of rectangle. That is given By :

$\dashrightarrow\sf Perimeter_{\:(rectangle)} = 2\bigg\{Length + Breadth\bigg\}$

⠀

On Substituting the given Values in the above formula, we get:

$\begin{gathered}\dashrightarrow\sf 130 = 2\Big\{(x + 5) + x\Big\}\\\\\end{gathered}$

On transposing '2' to the LHS, we get:

$\begin{gathered}\dashrightarrow\sf \cancel\dfrac{130}{2} = 2x + 5\\\\\end{gathered}$

$\begin{gathered}\dashrightarrow\sf 65 = 2x + 5\\\\\end{gathered}$

On transposing '5' to the LHS, we get:

$\begin{gathered}\dashrightarrow\sf 65 - 5 = 2x \\\\\end{gathered}$

$\begin{gathered}\dashrightarrow\sf 60 = 2x\\\\\end{gathered}$

$\begin{gathered}\dashrightarrow{\pmb{\sf{x = 30\;m}}}\\\\\end{gathered}[tex]</p><p> </p><p> </p><p></p><ul><li>We know that, value of <strong>x</strong> is<strong> '30'.</strong> Therefore, we'll substitute the value of x in given Length (30 + x) to find out the Length. Therefore —</li></ul><p>⠀</p><p></p><p>[tex]\begin{gathered}\twoheadrightarrow\sf Length = \Big\{x + 5\Big\}\\\\\end{gathered}$

$\begin{gathered}\twoheadrightarrow\sf Length = 30 + 5\\\\\end{gathered}$

$\begin{gathered}\twoheadrightarrow{\pmb{\sf{Length = 35\;m}}}\\\\\end{gathered}$

Hence,

• Length of the field = 35m
• Breadth of the field = 30m

∴ Therefore, the Length and Breadth of the rectangular field are 35m and 30m respectively.

________________________

________________________________

_____________________________________

⠀